'universally-praised' is formed in modern English from the adverb 'universally' and the past participle 'praised'. 'universally' comes ultimately from Latin 'universalis', and 'praise' comes from Old French 'preisier' (to value) / Late Latin 'pretiāre' (to value).

'universalis' (Latin) passed into Old French/Medieval Latin and then into Middle English as 'universal'; 'preisier' (Old French) became Middle English 'preisen' and later modern English 'praise'. The compound phrase 'universally praised' developed by combining the adverbial form of 'universal' with the past participle of 'praise'.

Originally, elements related to 'praise' often carried the sense 'to value or regard highly' (from 'price/value'); over time this shifted toward the modern sense 'express approval'. 'Universal' originally meant 'turned into one' or 'all as one' and evolved to mean 'applying to all'—so together they now mean 'praised by all'.